A Representation for Many Player Generalized Divide the Dollar Games
Why this work is in the frame
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Bibliographic record
Abstract
Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has n>2 players. Evolutionary algorithms can be used to evolve individual players for this generalized game but representation—i.e., a genome plus a move or search operator(s)—must be carefully chosen since it affects the search process. This paper proposes an entirely new representation called a demand matrix. Each individual in the evolving population now represents a collection of n players rather than just an individual player. Players use previous outcomes to decide their choices (bids) in the current round. The representation scales linearly with the number of players and the move operator is a variant of an evolution strategy. The results indicate that this proposed representation for the generalized divide the dollar game permits the efficient evolution of large player populations with high payoffs and fair demand sets.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it